Mathematical Modeling Measuring Self-Efficacy: A Scale Adaptation Study

Yıl 2024, Cilt: 11 Sayı: 1, 23 - 38, 31.03.2024

Erdoğan Yıldız , Sebahat Yetim

https://doi.org/10.17278/ijesim.1438228

Cited By: 1

Öz

Today, with science and technology developing at a dizzying pace, individuals need the information that will enable them to keep up with this pace; They need to have the skills to interpret it and transfer it to their daily lives. It is essential for individuals with these skills to have qualified teaching conditions and educational environments based on daily experiences. One of the methods that provide these environments is the mathematical modeling process. Students' success in mathematical modeling is closely related to students' self-efficacy beliefs. In this context, a study was carried out to adapt the mathematical modeling self-efficacy scale for students at secondary school level. The scale was adapted to 253 students and confirmatory factor analysis was performed. In the results obtained, it was determined that the scale used had a single-factor structure containing 17 items. Additionally, the reliability value of the scores obtained from the scale (Croanbach α = 0.89) was found to be sufficient. Among the values obtained because of the analysis, the χ2/df value is lower than 5, the AGFI and GFI values are greater than 0.85, and the RMSEA value is lower than 0.08, indicating the presence of model fit in terms of fit indices. As a result, it was determined that the mathematical modeling self-efficacy scale is a valid and appropriate scale for secondary school students.

Anahtar Kelimeler

mathematical modeling, self-efficacy scale, scale adaptation

Matematiksel Modelleme Öz yeterliklerin Ölçülmesi: Bir Ölçek Uyarlama Çalışması

Öz

Günümüzde baş döndürücü hızla gelişen bilim ve teknoloji ile birlikte bireylerin bu hıza ayak uydurabilmelerini sağlayacak bilgiyi; yorumlamaya, günlük yaşantılarına aktaracak becerilere sahip olmaları gerekmektedir. Bu becerilere sahip bireylerin nitelikli öğretim koşullarına, günlük yaşantılara dayalı eğitim-öğretim ortamlarının varlığına sahip olmaları şarttır. Bu ortamları sağlayan yöntemlerin biri de matematiksel modelleme sürecidir. Öğrencilerin matematiksel modellemedeki başarısı, öğrencilerin özyeterlik inancı ile yakından ilişkilidir. Bu bağlamda yapılan çalışmada, ortaokul düzeyinde öğrencilere yönelik matematiksel modelleme özyeterlik ölçeği uyarlama çalışması gerçekleştirilmiştir. Ölçek 253 öğrenciye uyarlanmış ve doğrulayıcı faktör analizi yapılmıştır. Elde edilen sonuçlarda, kullanılan ölçeğin 17 madde içeren tek faktörlü bir yapısı olduğu saptanmıştır. Ayrıca, ölçekten elde edilen puanların güvenirlik değeri (Croanbach α= 0,89) yeterli bulunmuştur. Analiz sonucunda elde edilen değerlerden, χ2/df değerinin 5'ten düşük olması, AGFI ve GFI değerlerinin 0,85'ten büyük olması ve RMSEA değerinin 0,08'den düşük olması uyum indeksleri açısından model uyumunun varlığını göstermektedir. Sonuç olarak, matematiksel modelleme özyeterlik ölçeğinin ortaokul öğrencileri için geçerli ve uygun bir ölçek olduğu belirlenmiştir.

Anahtar Kelimeler

: Matematiksel modelleme, öz yeterlik ölçeği, ölçek uyarlama

Kaynakça

• Akgün, L. ,Çiltaş, A.,Deniz, D.,Çiftçi, Z. & Işık, A. (2013). İlköğretim matematik öğretmenlerinin matematiksel modelleme ile ilgili farkındalıkları . Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi , (12) , 1-34 . https://doi.org/10.14520/adyusbd.410
• Algani, Y.M. (2022). Role, need and benefits of mathematics in the development of society. Journal for the Mathematics Education and Teaching Practices, 3(1), 23-29.
• Armutçu, Y. & Bal, A. P. (2023). The effect of mathematical modeling activities on students' mathematical modeling skills in the context of STEM education. International Journal of Contemporary Educational Research,10(1), 42-55. https://doi.org/10.33200/ijcer.1131928
• Avriel, M., & Golany, B. (1997). Mathematical programming for industrial engineers. Journal of the Operational Research Society, 48(3), 334. https://doi.org/10.1057/palgrave.jors.2600
• Ayotola, A., & Adedeji,T.(2009). The relationship between mathematics self-efficacy and achievement in mathematics. Procedia-Social and Behavioral Sciences, 1(1), 953–957. https://doi.org/10.1016/j.sbspro.2009.01.169
• Bailer-Jones, D. M. (2009). Scientific models in philosophy of science. University of Pittsburgh Press
• Bandalos, D. L., & Finney, S. J. (2010). Factor analysis: Exploratory and confirmatory. In G. R. Hancock& R. O. Mueller (Eds.), The reviewer's guide to quantitative methods in thesocial sciences (pp. 93-114). New York, NY: Routledge.
• Banks, J. (2014). Handbook of simulation: principles, methodology, advances, applications, andpractice. John Wiley & Sons.
• Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191-215.
• Bandura, A. (1986). Social foundations of thought and action: A Social cognitive theory. Englewood Cliffs, NJ: Prentice-Hall.
• Bandura, A. (1995). Self-efficacy in changing societies. New York: Cambridge University Press.
• Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman.
• Biehler, R., & Peter-Koop, A. (2007). Hans-Georg Steiner: A life dedicated to the development of didactics of mathematics as a scientific discipline. ZDM, 39, 3-30.
• Blum, W., & Leiß, D. (2007). Deal with modeling problems. Mathematical modelling: Education, engineering and economics-ICTMA, 12, 222.
• Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modeling and application, 1(1), 45-58.
• Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects—State, Trends and issues in mathematics instruction. Educational studies in mathematics, 22(1), 37-68.
• Bonotto, C. (2010). Realistic mathematical modeling and problem posing. In A. A. Editor & B. B. Editor (Eds.), Modeling students' mathematical modeling competencies (pp. 399-408). Springer.
• Borromeo-Ferri, R. (2006). The oretical and empirical differentiations of phases in the modeling process.Zentralblatt für didaktik der mathematik, 38(2), 86-95. https://doi.org/10.1007/BF02655883
• BorromeoFerri, R. (2007). Modelling problems from a cognitive perspective. In C. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modelling (ICTMA-12): Education, engineering and economics(pp. 260-270). Chichester: Horwood Publishing.
• Brauer, F., Castillo-Chavez, C., &Castillo-Chavez, C. (2012). Mathematical models in population biology and epidemiology (Vol. 2, No. 40). New York: springer.
• Briley, J. S. (2012). The relationships among mathematics Teaching efficacy, mathematics self-efficacy, and mathematical beliefs for elementary pre-service teachers. Issues in the undergraduate Mathematics Preparation of School Teachers ,5.http:// www. k12prep. math.ttu. edu /journal/5.attributes/haciomeroglu02/article.pdf
• Brown, T. A. (2015). Confirmatory factor analysis for applied research. Guilford Publications.
• Browne, M. W., Cudeck, R. (1992). Alternative ways of assessing model fit. Sociological Methods & Research, 21(2), 230-258.
• Baran Bulut, D. ve Türker, M. (2022). Ortaokul öğrencilerinin üslü ifadeler konusunda modelleme yeterliklerinin incelenmesi: Sarmal kitaplık problemi. Recep Tayyip Erdoğan Üniversitesi Eğitim Fakültesi Dergisi (REFAD), 2(2), 39-56.
• Bursal, M., Paznokas, L. (2006). Mathematics anxiety and preservice elementary teachers’ confidence to teach mathematics and science. School science and mathematics, 106(4), 173–179.https://doi.org/10.1111/j.1949-8594.2006.tb18024.x
• Byrne, B. M. (2013). Structural equation modeling with Mplus: Basic concepts, applications, and programming. routledge.
• Chan, E. C. M. (2009). Mathematical modelling as problem solving for children in the Singapore mathematics classrooms. Journal of Science and Mathematics Education in Southeast Asia, 32(1), 36-61.http://hdl.handle.net/10497/15726
• Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., &Schauble, L. (2003). Design experiments in educational research. Educational researcher, 32(1), 9-13.
• Creswell, J. W. (2014). Research design: Qualitative, quantitative, andmixedmethods approaches. Sage publications.
• De Pater, I. E., Van Vianen, A. E., Fischer, A. H., & Van Ginkel, W. P. (2009). Challenging experiences: Gender differences in task choice. Journal of Managerial Psychology, 24(1), 4-28.
• Doerr, H. M., Delmas, R., &Makar, K. (2017). A modeling approach to the development of students’ ınformal inferential reasoning. Statistics Education Research Journal, 16(2), 86-115.
• English, L. D., Ärlebäck, J. B., & Mousoulides, N. (2016). Reflections on progress in mathematical modeling research. In The second handbook of research on thepsychology of mathematics education (pp. 383-413). Brill.
• Erdoğan, F. (2019). İlköğretim matematik öğretmeni adaylarının matematiksel modelleme öz yeterliklerinin belirlenmesi. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 15(1), 118-130. https://doi.org/10.17860/mersinefd.480866
• Flegg, J., Mallet, D., & Lupton, M. (2012). Students' perceptions of therelevance of mathematics in engineering. International Journal of Mathematical Education in ScienceandTechnology, 43(6), 717-732. https://doi.org/10.1080/0020739X.2011.644333
• Galbraith, P. (2012). Models of modelling: Genres, purposes or perspectives. Journal of Mathematical Modelling and application, 1(5), 3-16.
• Genç, M. & Karataş, İ. (2017). Problem çözme süreçlerinde öğrencilerin modelleme seviyelerinin belirlenmesi . Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi , 18 (3) , 608-632 . Retrievedfrom https://dergipark.org.tr/tr/pub/kefad/issue/59420/853405
• Gravemeijer, K. & Stephan, M. (2002). Emergent models as an instructionaldesignheuristic. In K. Gravemeijer, R. Lehrer, B. Oers, & L. Verschaffel (Eds.), Symbolizing, modelingand tool use in mathematics education(pp. 145-169). Dordrecht, TheNetherlands
• Greefrath, G., &Vorhölter, K. (2016). Teaching and learning mathematical modelling: Approaches and developments from German speaking countries. Springer Nature.
• Fabrigar, L. R., Wegener, D. T., MacCallum, R. C. & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272-299
• Fink, A. (2003). How to sample in surveys. SAGE Publications, Inc., https://doi.org/10.4135/9781412984478
• Hair, J. F., Black, W. C., Babin, B. J. & Anderson, R. E. (2014). Multivariate data analysis (7th ed.). PearsonEducation.
• Hair, J. F., Anderson, R. E., Tatham, R. L. & Black, W. C. (1998). Multivariate data analysis(Vol. 5). PrenticeHall.
• Holenstein, M., Bruckmaier, G., &Grob, A. (2022). How do self‐efficacyand self‐concept impact mathematical achievement? The case of mathematical modelling. British Journal of Educational Psychology, 92(1), e12443. https://doi.org/10.1111/bjep.12443
• Hu, L.-t., & Bentler, P. M. (1999). Cut off criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. https://doi.org/10.1080/10705519909540118
• Kantz, H., & Schreiber, T. (2004). Nonlinear Time Series Analysis (2nd ed.). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511755798
• Khan, S., Grattan, K., & Finkelstein, L. (2007). Applications of modelling in engineering and technology. In Applications of Computer Technology to Dynamical Systems: Proceedings of the 7th ICATDS Conference (pp. 395-404). Elsevier. https://doi.org/10.1533/9780857099419.6.395
• Kelly, G. J. (2014). Discours epractices in science learning and teaching. In Handbook of Research on Science Education (Vol. 2, pp. 321-336). Taylor and Francis. https://doi.org/10.4324/9780203097267
• Kline, R. B. (2011). Principles and practice of structural equation modeling (3rd ed.). New York: Guilford Press.
• Koç, D., & Elçi, A. N. (2022). The Effect of mathematical modeling instruction on pre-service primary school teachers' problem solving skills and attitudes towards mathematics. Journal of Pedagogical Research, 6(4), 111-129. https://doi.org/10.33902/JPR.202217783
• Koğar, H., & Yılmaz-Koğar, E. (2015). Comparison of different estimation methods for categorical and ordinal data in confirmatory factor analysis. Journal of Measurement and Evaluation in Educationand Psychology, 6(2). 351-364.
• Koyuncu, İ. , Güzeller, C. O. & Akyüz, D. (2017). The development of a self-efficacy scale for mathematical modeling competencies. International Journal of Assessment Tools in Education , 4 (1) , 19-36 . DOI: 10.21449/ijate.256552
• Kurtuluş, A., & Öztürk, B. (2017). Ortaokul öğrencilerinin üstbilişsel farkındalık düzeyi ile matematik öz yeterlik algısının matematik başarısına etkisi. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 31(2), 762-778. https://doi.org/10.14582/DUZGEF.1840
• Leemis, L. M., & Park, S. K. (2006). Discrete-event simulation: A first course.Upper Saddle River: Pearson Prentice Hall.
• Lesh, R. A., Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematic teaching, learning, and problem solving. In R. Lesh& H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-34). Mahwah, NJ: Lawrence Erlbaum Associates.
• Lesh, R. & Zawojewski, J.S. (2007) Problem solving and modeling. In: Lester, F., (Eds.), Second handbook of research on mathematics Teaching and learning( pp. 763-802). Information Age Publishing, Greenwich, CT.
• Liu, X., Koirala, H. (2009). The effect of mathematics self-efficacy on mathematics achievement of high school students. NERA Conference Proceedings. 30.https://opencommons. uconn.edu/nera_2009/30
• Lord, F. M. (1980). Application of item response theory to practical testing problems. Hillsdale NJ: Erlbaum
• Luenberger, D. G. (2008). Optimization by vector space methods. John Wiley & Sons.
• Maddux, J. E. (2009). Self-Efficacy: The power of believing you can. In C. R. Snyder, & S. J. Lopez (Eds.), Handbook of positive psychology(pp.277-287). Oxford: Oxford University Press.
• Milli Eğitim Bakanlığı (MEB). (2018). Ortaöğretim matematik dersi öğretim programı. Erişim tarihi: 15 Şubat 2023, https://ttkb.meb.gov.tr/www/icerik_goster.php?id=284
• Molero Jurado, M. D. M., Pérez-Fuentes, M. D. C., OropesaRuiz, N. F., SimónMárquez, M. D. M., & Gázquez-Linares, J. J. (2019). Self-efficacy and emotional intelligence as predictors of perceived stress in nursing professionals. Medicina, 55(6), 237. https://doi.org/10.3390/medicina55060237
• National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Author.
• National Council of Teachers of Mathematics (NCTM). (2014). Principles and standards for school mathematics. https://www.nctm.org/ Standards –and –Positions /Principles -and-Standards /Principles-and Standards-for-School-Mathematics/
• National Governors Association Center for Best Practices & Council of Chief State School Officers(NGO, CCSSO) (2010).Common core state standards for mathematics. Washington, DC: Authors.
• Neuman, W. (2014) Social research methods: qualitative and quantitative approaches. Pearson, Essex, UK.
• Omreore, O. E., & Nwanzu, C. L. (2022). Examining the relationship among work-leisureconflict, coping self-efficacy, psychological flexibility and psychological wellbeing. Pakistan Journal of Commerce and Social Sciences (PJCSS), 16(2), 236-256. http://hdl.handle.net/10419/262370
• Özbek, G., & Köse, E. (2022). Matematiksel modelleme yeterlikleri ölçeği’nin geliştirilmesi ve psikometrik özelliklerinin belirlenmesi: Özel yetenekliler örneklemi. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 23(4), 853-871. https://doi.org/10.21565/ozelegitimdergisi.874247
• Özçakır-Sümen, Ö. (2022). An investigation of pre-service elementary teachers’ skills of Teaching numbers through digital story telling . Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi , 16 (1) , 1-16 . DOI: 10.17522/balikesirnef.1016564
• Özdemir, G., & Işık, A. (2015). Katı cisimlerin alan ve hacimlerinin matematiksel model ve matematiksel modelleme yöntemiyle öğretimine yönelik öğretmen görüşleri. K. Ü. Kastamonu Eğitim Dergisi, 23(3), 1251-1276.
• Özturan Sağırlı, M. ,Kırmacı, U. & Bulut, S. (2010). Türev konusunda uygulanan matematiksel modelleme yönteminin ortaöğretim öğrencilerinin akademik başarılarına ve öz-düzenleme becerilerine etkisi. Erzincan University Journal of Science and Technology , 3 (2) , 221-247. Retrieved from https://dergipark.org.tr/tr/pub/erzifbed/issue/6021/80652
• Schöber, C., Schütte, K., Köller, O., McElvany, N., & Gebauer, M. M. (2018). Reciprocal effects between self-efficacy and achievement in mathematics and reading. Learning and Individual Differences, 63, 1-11. https://doi.org/10.1016/j.lindif.2018.01.008
• Schreiber, J. B., Stage, F. K., King, J., Nora, A., &Barlow, E. A. (2006). Reporting structural equation modeling and confirmatory factor analysis results: a review. TheJournal of Educational Research, 99(6), 323–337. https://doi.org/10.3200/JOER.99.6.323-338
• Schoenfeld, Alan. (2011). Toward Professional developmentfor teachers grounded in a theory of decision making. ZDM: The International Journal on MathematicsEducation, 43. 457-469. https://doi.org/10.1007/s11858-011-0307-8
• Siebert, E. (2000). Looking ahead. Journal of CollegeScienceTeaching, 29(6), 373–375.
• Smith, J. P., diSessa, A. A., & Roschelle, J. (2011). Misconceptions reconceived: a constructivist analysis of knowledge in transition. The Journal of Learning Sciences, 20(1),37–80. https://doi.org/10.1080/10508406.2010.508029
• Stajkovic, A., & Luthans, F. (1998). Social cognitive theory and self-efficacy: Going beyond traditional motivational and behavioral approaches. Organizational Dynamics, 26(2),62-74. https://doi.org/10.1016/S0090-2616(98)90006-7
• Tabachnick. B., & Fidell. L. (2012). Using multivariatestatistics. Boston: Allynand Bacon.
• Tuğran, Z. (2015). İşbirlikli öğrenmenin lise öğrencilerinin matematik özyeterlik algısı ve başarısı üzerindeki etkileri. [Yükseklisans Tezi]. Çanakkale Onsekiz Mart Üniversitesi.
• Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of wordproblems. L. ErlbaumAssociates.
• Voinov, A., & Bousquet, F. (2010). Modelling with stakeholders. Environmental modelling& software, 25(11), 1268-1281. https://doi.org/10.1016/j.envsoft.2010.03.007
• Westbury, I., Hansén, S. E., Kansanen, P., &Björkvist, O. (2005). Teacher education for research‐based practice in expanded roles: Finland's experience. Scandinavian Journal of Educational Research, 49(5), 475-485. https://doi.org/10.1080/00313830500267937
• Yavuz Mumcu, H. & Cansız Aktaş, M. (2018). The investigation of the relationship between mathematical connections kill and self-efficacybelief. MATDER Matematik Eğitimi Dergisi, 1-8 . Retrieved from https://dergipark.org.tr/en/pub/med/issue/40936/452028
• Yılmaz, D. & Kesebir, G. (2023). Evaluation of mathematical modeling activities of 4th-grade students: thecase of experiential learning theory. Ankara University Journal of Faculty of Educational Sciences (JFES) , 56 (2) , 123-188 . https://doi.org/10.30964/auebfd.1037725
• Yum, S.-C., & Park, C.-Y. (2011). Mediating effect of learning strategy in the relation of mathematics self-efficacy and mathematics achievement: Latent growth model analyses. The Mathematical Education, 50, 103 - 118. https://doi.org/10.7468/ mathedu. 2011. 50.1.103
• Yurtsever, A. (2018). 6. sınıf öğrencilerinin matematiksel modelleme yeterlikleri, matematik başarıları ve tutumları arasındaki ilişki [Yüksek lisans tezi] Gazi Üniversitesi.
• Zawojewski, J.S., Magiera, M.T., &Lesh, R. (2013). A proposal for a problem-driven mathematics curriculum framework. The Mathematics Enthusiast.